Details

analyze4.8s

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	25%	75%	3
0%	25%	75%	4
0%	25%	75%	5
0%	25%	75%	6
0%	25%	75%	7
0%	25%	75%	8
1.6%	23.4%	75%	9
1.6%	23.4%	75%	10
1.6%	23.4%	75%	11
1.6%	23.4%	75%	12
1.6%	23.4%	75%	13
1.6%	23.4%	75%	14

sample5.4s

Algorithm

intervals

Results

3.5s	480×	body	5120	exit
763.0ms	271×	body	1280	overflowed
450.0ms	2070×	body	80	overflowed
311.0ms	214×	body	640	overflowed
108.0ms	125×	body	320	overflowed
93.0ms	3482×	pre	80	true
34.0ms	249×	body	80	valid
32.0ms	66×	body	160	overflowed
5.0ms	2×	body	1280	valid
2.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5035	43

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
0.7b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
2.4b	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

1192×	`add-exp-log_binary64`
692×	`pow-exp_binary64`
684×	`prod-exp_binary64`
593×	`div-exp_binary64`
344×	`pow-to-exp_binary64`
116×	`1-exp_binary64` `rec-exp_binary64`
42×	`*-un-lft-identity_binary64`
36×	`unpow-prod-down_binary64`
33×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `difference-of-squares_binary64`
4×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `sqr-pow_binary64` `inv-pow_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64` `flip-+_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64`

Counts

4 → 471

Calls

4 calls:

8.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
11.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
8.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
52.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
6.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
14.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
177.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

simplify111.0ms

Algorithm

egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5033	16646

prune140.0ms

Filtered

71 candidates to 483 candidates (-580.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	478	5	483
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	479	5	484

Merged error: 0.0b

Counts

484 → 5

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 s 1/2) (-.f64 c_p c_n))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64`
1×	`add-log-exp_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

simplify43.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5006	217

prune27.0ms

Filtered

15 candidates to 27 candidates (-80.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Merged error: 0.0b

Counts

32 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
1.0b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
11.2b	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))
11.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
38×	`log-prod_binary64`
36×	`add-sqr-sqrt_binary64`
15×	`associate--r+_binary64` `associate--l+_binary64`
14×	`pow1_binary64` `difference-of-squares_binary64`
12×	`distribute-lft-out--_binary64` `log-div_binary64`
10×	`add-cube-cbrt_binary64` `log-pow_binary64`
8×	`times-frac_binary64`
6×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `div-inv_binary64`

Counts

4 → 100

Calls

4 calls:

5.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
5.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
31.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))
13.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
11.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
25.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))
16.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4910	1897
1	4910	1897

prune155.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	0	3
Picked	1	0	1
Done	1	0	1
Total	115	2	117

Merged error: 0b

Counts

117 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 c_n (-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))))))
0.1b	(log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))))
0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
11.2b	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
67×	`*-un-lft-identity_binary64`
55×	`log-prod_binary64`
38×	`difference-of-squares_binary64`
33×	`associate--l+_binary64`
24×	`times-frac_binary64`
20×	`distribute-lft-out--_binary64`
15×	`pow1_binary64`
14×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`associate--r+_binary64` `add-cube-cbrt_binary64`
10×	`log-div_binary64`
9×	`log-pow_binary64`
8×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `associate--r-_binary64` `add-cbrt-cube_binary64` `div-inv_binary64`
4×	`sub-neg_binary64`
3×	`associate-l_binary64`
2×	`associate--l-_binary64` `diff-log_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 136

Calls

4 calls:

20.0ms	(*.f64 c_n (-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))))))
14.0ms	(log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))))
11.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
27.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(*.f64 c_n (-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))))))
15.0ms	(log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))))
6.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
25.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4903	3399
1	4903	3399

prune163.0ms

Filtered

87 candidates to 148 candidates (-70.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	148	2	150

Merged error: 0b

Counts

150 → 2

regimes141.0ms

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	223	38
1	223	38

end0.0ms

sample10.7s

Algorithm

intervals

Results

6.9s	982×	body	5120	exit
1.5s	558×	body	1280	overflowed
927.0ms	4401×	body	80	overflowed
691.0ms	482×	body	640	overflowed
218.0ms	264×	body	320	overflowed
180.0ms	7327×	pre	80	true
65.0ms	497×	body	80	valid
61.0ms	129×	body	160	overflowed
8.0ms	4×	body	1280	valid
2.0ms	2×	body	640	valid
2.0ms	6×	body	160	valid
1.0ms	2×	body	320	valid

Details

analyze4.8s

sample5.4s

simplify56.0ms

prune3.0ms

localize21.0ms

rewrite125.0ms

series211.0ms

simplify111.0ms

prune140.0ms

localize6.0ms

rewrite9.0ms

series10.0ms

simplify43.0ms

prune27.0ms

localize29.0ms

rewrite57.0ms

series62.0ms

simplify65.0ms

prune155.0ms

localize28.0ms

rewrite78.0ms

series89.0ms

simplify100.0ms

prune163.0ms

regimes141.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample10.7s

Profiling